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Xia et al. (2014). “Modeling straw ring-die briquetting,” BioResources 9(4), 6316-6328. 6316
Modeling of a Straw Ring-die Briquetting Process
Xianfei Xia, Yu Sun,* Kai Wu, and Qinghai Jiang
Efficient utilization of biomass resources is crucial for providing renewable energy and mitigating the risk of environmental pollution caused by crop straw burning in China. Straw ring-die briquetting forming is a convenient densification technology to make the low density biomass into briquette fuel; however, the energy consumption of this process is still a challenge. Productivity and torque modeling were carried out in this study on the basis of theoretical derivation. Generally, the straw briquetting process is divided into a compression deformation stage and an extrusion forming stage with the die structure (ring die and roller radius ratio λ) and friction angle φ being the main factors that affect the productivity. Mechanical modeling based on material compaction and calculation modeling based on die-hole pressure were considered for the calculation of σαx in the torque model. A calculation case was then conducted according to the theoretical model, and actual productivity and torque testing were performed for validation purposes. Results show that this deduced productivity model is successful because the deviation is 4.61%. The torque model determined by the calculation model based on die-hole pressure had a better accuracy with a deviation of 6.76%.
Keywords: Briquetting; Straw; Productivity; Mechanical modeling; Torque
Contact information: School of Mechanical Engineering, Nanjing University of Science and Technology,
No. 200 Xiaolingwei, Nanjing 210094, China;
* Corresponding author: [email protected]
INTRODUCTION
With the growing energy crisis and environmental problems (Tuo 2013), utilization
of biomass has gained a lot of attention. Because straw contains a large amount of useful
lignin and cellulose, efficient utilization of this abundant resource is crucial for providing
bio-energy and mitigating the risk of environmental pollution. This research presents a
study on the analysis of machinery for handling biomass for energy generation, in particular
transforming straw materials to briquettes. The need for this transformation has been
widely justified, as shown by other works (Panwar et al. 2010). The transformation has two
processes: densifying the low density straw and rolling it to a form for easy transportation.
The device to make this transformation is called ring-die briquetting (R-D for short). The
R-D system has many advantages such as versatility and flexibility to different types of
low density straws compared with the system of screw bar pressing and piston pressing
(Stelte et al. 2012), but the shortcoming of high energy consumption during the briquetting
process still exists (Zhang et al. 2008).
For all the biomass briquetting systems, the average energy consumption is the most
important evaluation index; it is calculated by the ratio of power consumption and
productivity (Ståhl and Berghel 2011). Power consumption is the product of speed (ring
die rotational speed or roller rotational speed) and torque (Cong et al. 2013), while the
speed is generally determined in advance (Yao et al. 2013). When the raw material property
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Xia et al. (2014). “Modeling straw ring-die briquetting,” BioResources 9(4), 6316-6328. 6317
remains unchanged, the reasonable parameter design is the main way to reduce energy
consumption. So it is necessary to establish the productivity and torque model to describe
the energy consumption of the R-D system’s actual working process.
Some studies have focused on the forming mechanism (Adapa et al. 2013; Gillespie
et al. 2013), and others on fuel quality (Kaliyan and Morey 2010; Karunanithy et al. 2012).
Studies have reported on the energy consumption with this process in a laboratory setting
with a single pelleter unit (Ghadernejad and Kianmehr 2012; Hu et al. 2013; Song et al.
2014). It is well known that laboratory studies on such a process can hardly be extended to
the industrial setting. Hu (2013) and Holm et al. (2011) obtained the theoretical models to
describe the forming pressure by extrusion testing respectively; these models are the bases
of force analysis and torque calculation. Duan et al. (2013) made an optimization analysis
of energy consumption and productivity of the R-D briquetting machine by factory test,
but the corresponding theoretical calculation models were not established. Yao et al. (2013)
developed a new vertical R-D briquetting machine to increase productivity and reduce
energy consumption; however there was no theoretical calculation of its productivity; and
the forming pressure was considered to be constant in the power consumption analysis.
Although Ståhl and Berghel (2011) studied the energy consumption of a pilot-scale
production of wood fuel pellets, the testing object was a flat die machine.
Cong et al. (2013) and Wu et al. (2013) built up the productivity and torque models
of a biomass pellet mill; however the method to calculate the pressure in the forming zone
was not comprehensive enough. In addition, there are some obvious differences between a
biomass briquetting machine and a pellet mill: the ring die of pellet mill is the driving
component and it rotates under normal condition, while the ring die of a briquetting
machine is fixed on the frame, and the driving component is roller; the pellet mill ring die
is usually horizontal placement, whereas the briquetting machine ring die is vertical. The
motion state and force condition of the main working parts are various.
Therefore, the current models are not applicable. Modeling the R-D process to more
accurately predict its productivity and driving torque is very important in reasonably
designing or optimizing the R-D briquetting machine. The objective of this work was to
present a model to calculate the productivity and driving torque for the R-D process for
straw material. The paper is organized as follows: first, a brief introduction for the working
principle for the straw briquetting process is given. Then, the model for estimating
productivity rate and for computing the torque will be presented. Later, a case study with
the experiment on an industrial scale is presented to verify the model. Finally, some
conclusions are given.
EXPERIMENTAL
The Working Principle of the Straw R-D Process The working principle of the straw R-D process is shown in Fig. 1. The ring die is
fixed on the machine. When the straw material is fed into the cavity formed by the ring die
and press roller, the roller (driven by a spindle) starts to rotate and grab the material. The
material then is compressed and squeezed into the die holes gradually. Lignin and cellulose
contained in the raw material begins to soften and then bond together under the action of
frictional heat. After a specific holding time the straw is extruded out as a briquetting fuel
with a certain shape (diameter of 20 to 30 mm, length of 40 to 80 mm) and density (0.8 to
1.1 g/cm3).
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Xia et al. (2014). “Modeling straw ring-die briquetting,” BioResources 9(4), 6316-6328. 6318
Fig. 1. Schematic of the straw R-D process
Model for Estimating the Productivity of the R-D Process The material grabbing condition
The frictional effect that exists between the ring die, roller, and the material is the
key factor that influences the straw briquetting process. Before the material is grabbed, it
is in a sliding friction state together with the roller. There are three forces acting on the
forming material: the pressure force Nr, the friction force Fr of the roller surface on the
straw material, and the pressure force NR of the compressed straw layer on the loose
material. The closer the minimum spacing between the roller and ring die, the greater the
value of NR. When Fr is greater than the circumferential tangential component of NR, the
material is grabbed. The grabbing process is illustrated in Fig. 2a.
Fig. 2. Schematic diagram of the straw grabbing process. (a) The material grabbing process and (b) the force analysis of the grabbed straw
Force analysis is carried out for a small part of material that is about to be grabbed.
A coordinate system was established as shown in Fig. 2b. When decomposing NR along the
x and y directions and when the grab condition is met, Eq. 1 is established.
sinr RF N (1)
Based on the force equilibrium condition, Nr=NRcosθ; Nr and Fr follow the
relationship Fr=fNr, where f is the friction coefficient between the material and the roller,
and tanφ=f, where φ is the friction angle. From Eq. 1, Eq. 2 then is set up.
tan tan (2)
a b
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φ is a fixed constant once the material property and roller surface state are
determined. In triangle OO1K and according to the sine theorem, β can be determined by
Eq. 3.
arcsin sinr
R r
(3)
In Fig. 2a, α=β+θ, which means that in the range of α, the straw material is grabbed
and compressed. Set R/r =λ, and since φ and θ are in the range of 90°, αmax can be expressed
as Eq. 4. The value of αmax was affected by friction angle φ and λ and a larger αmax value
corresponds to a bigger volume of the compressed raw material. There was a positive
correlation between briquetting efficiency and αmax.
max
sinarcsin
1
(4)
The Model
The variation trend of productivity is considered with reference to the change of α.
As shown in Fig. 2, material starts to be grabbed at point K, with a material height of hmax,
and hmax=R—OK. In triangle OO1K, OK can be determined by the cosine theorem, and hmax
is calculated by Eq. 5.
2
max max2 2 1 cosh r (5)
Then productivity Q (average material flow per hour through the ring die) can be
calculated by the following Eq. 6,
22
maxQ Kn B R R h
(6)
where n is spindle speed (r/min), ρ is material initial density (g/cm3), B is the effective
working width of the roller (mm), ε is the opening ratio of the ring die, K is the total number
of rollers, ξ is the material effective fill factor, and ξ is the correction factor of Eq. 6 with
a general value of 0.4 to 0.7.
Taking Eq. 4 and Eq. 5 into Eq. 6, and unifying the dimensions, the productivity Q
can be determined using Eq. 7.
2
10
2
sin1.2 10 1 1 cos( arcsin )
1
RQ Kn B
(7)
It can be seen from Eq. 7 that the productivity Q is mainly related to die structure
(ring die and roller radius ratio λ) and friction angle φ. For the straw R-D machine, the λ
value is generally between 2 and 4. The friction coefficient between the straw material and
roller are generally between 0.4 and 0.5(φ 20 to 30°). Taking ξ=0.5, ε=0.85, n=160 r/min,
B=30 mm, ρ=0.075 g/cm3, R=320mm, φ=20~30°, and λ=2~4, and using Eq. 7, the variation
of Q is shown in Fig. 3.
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Fig. 3. The variation trend of productivity Q
It can be seen from Fig. 3 that a larger φ and smaller λ corresponds to a higher
productivity. It should be noted that the actual productivity Q will be different than the
theoretical calculation from Eq. 7 due to the impact of material property, uniformity of the
feeding process, and other various aspects.
Model for Mechanics of the Briquetting Process Partition of the forming process
Once the material has been grabbed and completely compressed into the die holes,
the forming process can be divided into two phases: the compression deformation stage
and the extrusion forming stage. The compression deformation stage can be described as
loose material filling the cavity and gradually compacting after the grabbing condition has
been met. The pressure of the roller increases rapidly, and then straw material is pushed
into a smaller gap region by the frictional force of the roller surface. Material density
increases until reaching the requirement during this process. The extrusion forming stage
begins once the required density is achieved. Straw is gradually pushed into the die holes
under the strong pressure from the roller. The material will not be further compacted in this
phase, and the applied pressure is maintained constant and only the shape changes (Wu et
al. 2013). The partition is shown in Fig. 4 (0 to α1 is the extrusion forming zone, and α1 to
αmax is the compression deformation zone).
Fig. 4. Schematic of the partition
Assuming that the material starts compressing at point K and reaches the required
density ρ1 at point K1, the material height here is h1 and wrap angle is α1. Since 2R≫h1 and
2R≫h, according to the productivity model, Eq. 8 was established.
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01 max
1
h h
(8)
Using Eq. (5), h1 can be evaluated; therefore, the value of α1 can be obtained by Eq.
(9).
0 max 0 max
1 1
1
2
arccos 12 2
h h
r r
(9)
After the partition is determined, a further force analysis of these two areas should
be accomplished.
Force analysis of the roller
The active component of the straw R-D machine is the roller, while in the case of a
pellet mill it is the ring die. There are some certain differences of the force conditions. The
forces acting on the roller include F and N, which are the forces that the driving shaft acts
on the center of the roller; N1 and N2 represent the pressure generated on the surface of the
roller and on the two opposite direction friction forces F1 and F2, and are attributed to the
material’s compaction in compression deformation and extrusion forming regions
respectively. The directions of friction forces F1 and F2 are contrary in the two areas for
the following reason: the roller spins around point O driven by the spindle, with the straw
material generating the friction force F2 to prevent the roller from turning. Under the action
of F2, the roller rotates in the counter-clockwise direction, so the straw material is grabbed
and a frictional force F1 opposite to the rotation direction is generated. The force condition
is shown as Fig. 5.
Fig. 5. Force condition of the roller
According to the moment equilibrium condition in Fig. 5, the moment of each force
to point O1 is zero. Then it can be concluded that F1=F2. This means that the frictional force
value of the compression deformation and extrusion forming zones are equal. This analysis
well explains the rotation behavior of the roller in normal work state.
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Solution of driving torque T
In the compression deformation zone, stress σαx increases from zero to the
maximum value gradually, but in the extrusion forming zone stress σmax remains constant.
In order to determine the value of N1 and N2, force analysis of a small segment of the roller
was performed (Jin 2010) and is shown in Fig. 6.
Fig. 6. Solving schematic diagram of N1 and N2
Assuming that the stress is σαx, then the pressure force dN acting on the roller can
be expressed as Eq. 10.
xdN Brd (10)
The quantities αN2 and αN1 are the central angles of resultant forces N2 and N1, respectively
(Fig. 5). They can be determined by Eqs. 11 and 12.
2 1 2N (11)
1 1
1 11
x
N
x
dN d
dN d
(12)
Because the working surface of the roller has a certain curvature, dN should be
decomposed along the αN1 (or αN2) direction for solving the resultant force N1 (or N2), as
shown in Fig. 7.
Fig. 7. Decomposition diagram of the roller force
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N1 and N2 can then be calculated by Eqs. 13 and 14 (Wu and Sun 2013).
max 1
1 1
1 1 1cos( ) cos( )N
N
x N x NN Brd Brd
(13)
21
2
2 max 2 max 2
0
cos( ) cos( )N
N
N NN Brd Brd
(14)
The moment of each force to point O can be represented by Eq. 15.
1 1 2 2
1 1 2 2
cos cos
sin sin 0
N N
N N
F R r F r R r F r R r
N R r N R r
(15)
Since F1=F2 and F2=N2f, F can be determined by Eq. 16.
2 2 1 1 1 2 2cos cos sin sinD N N N NF N f N N
(16)
Then, driving torque T can be calculated by Eq. 17.
2 ( )T F R r (17)
Calculation Model of σαx
Determining the value of torque T requires the solution of σαx. Typically, there are
two main calculation methods for determining σαx: a mechanical model based on material
compaction and a calculation model based on die-hole pressure. The main differences
between these two models are the change trend of σαx and value of σmax.
The mechanical models based on material compaction, model 1, are listed in Table
1. An exponential relationship has been discovered between pressure and compacted
density, as Table 1 shows.
Table 1. Mechanical Model Based on Material Compaction
No.
Representative scholars Calculation model
1 Skalweit (Huo 2013) 𝑃 =𝑝0𝛾0
b𝛾b
2 Faborode (Faborode and O’Callaghan 1986)
𝑃 =𝐴𝛾0𝑏
[e𝑏(𝛾−1) − 1]
3 Panelli-Filho (Panelli and Filho 2001) ln (1
1 − 𝛾) = 𝑏 + 𝐴√𝑃
4 Jianjun Hu (Hu 2008) 𝑃 = 𝐴e𝑏x Note: P is pressure, γ is compacted density, p0 is initial stress, γ0 is initial density, A and b are test coefficients, and x is compaction displacement
In the Hu model (Hu 2008), rice straw was compressed and the test coefficients
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were obtained. The research object in this study was rice straw, so this model was adopted
and σαx can be described by Eq. 18.
max( )x
b h hAe
(18)
Based on the elastic-plastic mechanic theory, Holm et al. (2011) provides an
effective method for calculating the die-hole pressure (Model 2). The pressure σmax at the
inlet of the die hole can therefore be calculated by Eq. (19).
2 /0 0max
hf L r
L e
(19)
where μ is Poisson’s ratio; σ0 is pre-stressing pressure; f is friction coefficient; rh is die hole
diameter; and L is die hole length. The assumption: raw material is elastic and orthotropic
material; the differential force is constant over the cross-sectional area πr2.
Wu et al. (2013) indicated that the change law of pressure σαx is in accordance with
a quadratic curve model within the scope of α1 to α. The assumptions were as follows: ring
die and roller were rigid bodies; body force was not taken into account; the material was
distributed on the ring die uniformly; and the modified Drucker-Prager-Cap model was
adapted. So σαx can be calculated by Eq. 20 (ht=hmax - h1).
2maxmax2
( )xt
h hh
(20)
A case analysis of the theoretical model
According to the formulas above, a theoretical calculation was carried out in
accordance with the actual parameters. Calculation conditions are as follows. Equipment
structure parameters: r = 320 mm, R = 720 mm, B = 30 mm, L = 165 mm, and rh = 30 mm.
Material property parameters: ρ0 = 0.075 g/cm3, ρ1 = 1.02 g/cm3, φ = 25° (f = 0.466), and u
= 0.45. Parameters of the Hu model are A = 0.1002 and b = 0.0710 (Hu 2008). The
correction factor ζ in Eq. (6) and pre-stressing pressure σ0 in Eq. (18) have been obtained
through testing prior to the calculation (ζ is 0.47 and σ0 is 0.1895 MPa). Variation of σαx
based on two models in the compression deformation zone is shown as Fig. 8. Calculation
results of the two models are shown in Table 2.
Fig. 8. Variation of σαx in the compression deformation
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Table 2. Calculation Results of the Two Models
Parameter name Model 1 Model 2
Q (t/h) 1.089
αmax (°) 44.761
h (mm) 53.496
h1 (mm) 3.934
α1 (°) 12.066
αN1 (°) 21.074 21.499
αN2 (°) 6.033 6.033
N1 (N) 11570.612 9106.450
N2 (N) 7019.541 7660.822
F (N) 5098.756 4371.149
T (N•m) 4079.005 3402.711
Experimental Verification To verify the accuracy of the theoretical model, productivity and torque testing
were completed. Productivity testing was performed by digital electronic weight
(according to the agricultural industry criteria of China NY/T 1883-2010), and torque
testing of the drive motor’s shaft was implemented by the Bichuang wireless torque
measurement system (Beijing Bichuang Technology Co., Ltd., Beijing, China). In this
system, strain gauges were symmetrically arranged to eliminate the impact of bending
moment. The arrangement method and bridging form of strain gauge are shown in Fig. 9a.
Experimental equipment and materials include a ring-die straw briquetting machine
(9EYK1800; Jiangsu ENERGY Renewable Resources Co., Ltd., Taizhou, Jiangsu
Province, China), wireless nodes (TQ201; Beijing Bichuang Technology Co., Ltd., Beijing,
China), digital electronic weighter, special torque strain gages, wireless gateway, special
torque analysis software, sandpaper, alcohol cotton, glue, scissors, and fiber tape. The raw
material was rice straw harvested in the autumn of 2013 in Jiangyan, Jiangsu Province,
China. The straw was chopped, with particle size of 2 to 20 mm and moisture content of
15 to 21%, and briquetted without adding any binders. Experiments were conducted at an
industrial factory (Jiangsu ENERGY Renewable Resources Co., Ltd., Taizhou, Jiangsu
Province, China). Figure 9b shows the torque testing site.
Fig. 9. Torque testing program. (a) Arrangement and bridging form of strain gauge and (b) torque
testing site
a
b
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RESULTS AND DISCUSSION
Figure 10 shows the torque testing data. The average value of the motor shaft’s
testing torque TM was 0.729 kN•m and the roller spindle’s testing torque T was 3.187 kN•m
(T = iηTM, where η is transmission efficiency and i is transmission ratio; i = 4.6, η = 0.95
for the testing machine).
Fig. 10. Experimental torque data. Data is expressed as average ± SD
Experimental results and deviations are shown in Table 3. The testing value of
productivity Q was 1.041 t/h, the average of three test results. There was a deviation
(between the calculated and tested values) of 4.61% due to the impact of the feeding
process (rice straw contains lignin and cellulose; they are very soft and can easily entwine
together. Therefore, small groups of straw material are formed one after another during the
feeding). Fluctuation of torque T in Fig. 10 shows the non-uniformity of the actual feeding
process. Therefore, the deviation is within an acceptable range. Compared with Model 1,
Model 2 exhibited a better accuracy with the deviation (between the calculated and tested
values) of 6.76%, which means that Model 2 can describe the mechanical behavior of straw
actual compression process more accurately.
Table 3. Experimental Results and Deviation
Category Productivity Q (t/h) Torque T (N•m)
Tested value 1.041 3187.153
Calculated value 1.089 Model 1 Model 2
4079.005 3402.711
Deviation 4.61% 27.98% 6.76%
CONCLUSIONS
This work was aimed at reducing the energy consumption and improving the
efficiency of the straw briquetting process. Based on the theoretical derivation and
experimental validation, the key conclusions are summarized as follows:
1. Productivity Q is higher at smaller die structure (radius ratio λ) and larger friction angle
φ. The forming process can be divided into two stages: compression deformation and
then extrusion forming. Two stages are corresponding at 0 to α1 and α1 to αmax during
the process, respectively.
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2. The forces acting on the roller include F and N, for which the driving shaft acts on the
center of the roller; N1 and N2 represent the pressure generated on the surface of the
roller and on the two opposite direction friction forces F1 and F2.
3. In the compression deformation zone, stress σαx increases from zero to the maximum
value gradually, but in the extrusion forming zone stress σmax remains constant. There
are two main calculation methods for σαx: a mechanical model based on material
compaction and a calculation model based on die-hole pressure.
4. Experimental validation indicates that the productivity model was successful since the
deviation was calculated to be 4.61%. The torque model determined by the calculation
model based on the die-hole pressure had a better accuracy with a deviation of 6.76%.
ACKNOWLEDGMENTS
This work was supported by The Project of Six Talents Peak of Jiangsu Province
(2010-JXQC-080), The Natural Science Foundation of Jiangsu Province (BK2011706),
and The Prospective Industry-Study-Research Cooperation Foundation of Jiangsu
Province (BY2012023).
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Article submitted: July 10, 2014; Peer review completed: August 9, 2014; Revised
version received: August 25, 2014; Accepted: August 26, 2014; Published: September 2,
2014.